Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 16 - Section 16.6 - Parametric Surfaces and Their Areas - 16.6 Exercise - Page 1120: 20



Work Step by Step

The vector equation of a plane containing the vectors $b_{1}$ and $b_{2}$ and containing a point with position vector $a$ is $r(u,v)=a+ub_{1}+vb_{2}$ The plane contains the vectors $\lt 2,1,4\gt$ and $\lt -3,2,5\gt$ and the plane contains the point, whose position vector is $\lt0,-1,5\gt$ Therefore, the vector equation of the plane is $r(u,v)=\lt0,-1,5\gt+u\lt2,1,4\gt+v\lt-3,2,5\gt$ $r(u,v)=\lt0,-1,5\gt+\lt2u,u,4u\gt+\lt-3v,2v,5v\gt$ This implies $r(u,v)=\lt2u-3v,-1+u+2v,5+4u+5v\gt$ Hence, the parametric representation of the plane is $x=2u-3v,y=-1+u+2v,z=5+4u+5v$
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